Training recurrent neural networks with noisy input measurements

Under some regularity conditions, dynamic systems can be approximated to any accuracy by recursive neural networks that are properly trained on input/output data of the dynamic system. Noisy measurements of outputs can be used instead of the true outputs without much loss of approximation accuracy. However, the same cannot be said for noisy measurements of inputs. The idea of errors-in-variables (EIV) for regression in statistics is borrowed for the training of recursive neural networks using noisy input measurements. In the training, the inputs and the weights of the neural network are simultaneously estimated. An EIV criterion and an associated algorithm for such training is presented, A simulation study shows that significant improvements result from the use of the EIV criterion and algorithm